Fully Nonlinear Wave Current Body Interaction Analysis by a Harmonic Polynomial Cell Method

Abstract

A new numerical 2D cell method has been proposed by the authors, based on representing the velocity potential in each cell by harmonic polynomials. The method was named the harmonic polynomial cell (HPC) method. The method was later extended to 3D to study potentialflow problems in marine hydrodynamics. With the considered number of unknowns that are typical in marine hydrodynamics, the comparisons with some existing boundary elementbased methods, including the fast multipole accelerated boundary element methods, showed that the HPC method is very competitive in terms of both accuracy and efficiency. The HPC method has also been applied to study fullynonlinear wavebody interactions; for example, sloshing in tanks, nonlinear waves over different seabottom topographies, and nonlinear wave diffraction by a bottommounted vertical circular cylinder. However, no current effects were considered. In this paper, we study the fullynonlinear timedomain wavebody interaction considering the current effects. In order to validate and verify the method, a bottommounted vertical circular cylinder, which has been studied extensively in the literature, will first be examined. Comparisons are made with the published numerical results and experimental results. As a further application, the HPC method will be used to study multiple bottommounted cylinders. An example of the wave diffraction of two bottommounted cylinders is also presented.